Question : Find $\frac{0.04}{0.03}\text{of}\frac{( 3\frac{1}{3} – 2\frac{1}{2} ) ÷ \frac{1}{2} \space \text{of} \space 1\frac{1}{4} }{\frac{1}{3} + \frac{1}{5} \space \text{of} \space \frac{1}{9}}$.
Option 1: $1$
Option 2: $5$
Option 3: $\frac{1}{5}$
Option 4: $\frac{1}{2}$
Correct Answer: $5$
Solution :
Given: $\frac{0.04}{0.03}\text{of}\frac{( 3\frac{1}{3}– 2\frac{1}{2}) \space ÷ \space \frac{1}{2} \space \text{of} \space 1\frac{1}{4} }{\frac{1}{3} + \frac{1}{5} \space \text{of} \space \frac{1}{9}}$
= $\frac{4}{3}\text{of}\frac{( \frac{10}{3} – \frac{5}{2}) ÷ (\frac{1}{2} × \frac{5}{4})}{\frac{1}{3} + \frac{1}{5} × \frac{1}{9}}$
= $\frac{4}{3}\text{of}\frac{( \frac{20 – 15}{6}) ÷ (\frac{1}{2} × \frac{5}{4} )}{\frac{1}{3}+ \frac{1}{5} × \frac{1}{9}}$
= $\frac{4}{3}\text{of}\frac{\frac{5}{6} ÷ \frac{5}{8}}{\frac{1}{3} + \frac{1}{45}}$
= $\frac{4}{3}\text{of}\frac{\frac{5}{6}×\frac{8}{5}}{\frac{15 + 1}{45}}$
= $\frac{4}{3}\text{of}\frac{\frac{8}{6}}{\frac{16}{45}}$
= $\frac{4}{3}$×$\frac{8}{6}$×$\frac{45}{16}$
= $5$
Hence, the correct answer is $5$.
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